There is well known an automatic transmission with a plurality of shift ranges in which switching from a forward drive range as one of the shift ranges to a reverse drive range as one of the shift ranges is inhibited during a forward running. For example, JP-2003-166643A discloses a vehicle control apparatus configured to inhibit switching from the forward drive range to the reverse drive range by operation of an operator of a vehicle when the vehicle runs at a speed not lower than a given value, and to allow the switching from the forward drive range to the reverse drive range when the vehicle runs at a low speed, for thereby avoiding shock caused by a sudden change of running speed of the vehicle in the event of an erroneous shift range switching by the vehicle operator, while assuring operational convenience, for example, in a so-called “going back and forth” by allowing the switching during running at a low speed.